Why did Sasuke's brother kill his whole family in Naruto?

Because it is an internal secret. His brother reached an agreement with Madara for the stability of Konoha, but he had to sacrifice his family, so Itachi could only serve as a judge, but Sasuke didn't know about this, but Itachi really couldn't bear to kill his brother, so for It allows him to grow faster and have strength, so Sasuke can only kill him if he thinks he has killed his family, so that he can have the motivation to live. Naruto has a family, and his father is the 4th generation but has passed away.